ON AUTOMATIC SEEKING OF OPTIMAL STEADY-STATES IN BIOCHEMICAL PROCESSES Georges Bastin ∗,1 Dragan Neˇ si´ c ∗∗ Ying Tan ∗∗ Iven Mareels ∗∗ ∗ Center for Systems Engineering and Applied Mechanics, Universit´ e Catholique de Louvain, 4, Avenue G. Lemaitre, 1348 Louvain-La-Neuve, Belgium. ∗∗ The Department of Electrical and Electronics Engineering, University of Melbourne, Melbourne, VIC 3010, Australia. Abstract: It is discussed how the automatic seeking of optimal steady states in biochemical reactors can be achieved by using non-model based extremum-seeking control with semi-global practical stability and convergence properties. A special attention is paid to processes with multiple steady-states and multivalued cost functions. Copyright c IFAC 2007 Keywords: Biochemical Process, Extremum Seeking, Multivalued cost function. 1. INTRODUCTION We are concerned with automatic seeking of opti- mal steady states in biochemical reactors when the process kinetics are unknown to the user. We want to examine how this objective can be achieved by using non-model based extremum- seeking control. The goal of the paper is threefold : 1) To provide a clear characterization of the steady-states that achieve an optimal trade-off between yield and productivity maximization in biochemical processes. 2) To show how this optimization problem can be solved by using feedback extremum seeking (ES) 1 Research supported by National ICT Australia (NICTA) and by the Belgian Programme on Interuniversity Attrac- tion Poles (IAP V/22). control with semi-global stability and convergence properties. 3) To show that the analysis can be extended to situations with multiple steady-states and a multivalued cost function by using generalized singular perturbation results as presented, for example, in Teel et al. (2003). Here the Aumann integral (Aumann (1965)) is used to define the average of all possible behaviors of the slow system and as a result the average of the slow system is a differential inclusion. We believe that viewing the problem in this manner is novel and could lead to solutions of various other problems not considered in this paper. In this short communication, for the sake of sim- plicity and clarity, we limit ourselves to processes where a single monomolecular irreversible reaction takes place. However, even though we deal only with the simplest situation, the issues that emerge Preprints of the 7th IFAC Symposium on Nonlinear Control Systems 21-24 August, 2007, Pretoria, South Africa 814